Andrew Hartley poses the question 'Does the Christian faith have anything distinctive to say ... about the foundations or practice of statistics as a science?' His answer is a resounding yes. In this book he shows us how. As he does so he exposes the dogma that statistics is religiously neutral as being a religious belief. If such a claim seems intriguing or even outrageous, then this book is for you.

He maintains that statistics has for the most part been controlled by non-Christian, humanist beliefs. His desire is to see the Christian faith integrated with statistics; hence the descriptive, if not snappy, title of the book.

Hartley claims to write for a wide audience, yet the mathematical equations may put off many arts students, which is a pity as they would benefit from this excellent introduction, as Hartley writes clearly and explains the difficult mathematics well. Though there were one or two places I had to re-read and read slowly!

Hartley begins by looking at four different paradigms within statistics: direst and indirect frequentism, subjective and objective bayesianism.

He then provides a brief overview of Dooyeweerd's philosophy - the philosophy of the law idea (PLI). This includes the religious control of any and all sciences, the modal aspects - their irreducibility and inter-aspect coherence - and the role of religious groundmotives.

He looks in more depth at one religious groundmotive, the nature freedom motive. This has two main poles: the nature or science ideal and the personality ideal. The former emphasises nature and the latter freedom. He sees how these apply to the statistical paradigms. The nature ideal (over)emphasises and absolutises the mathematical aspects of reality, this is seen in direct frequentism and objective bayesianism. These paradigms tend to be the most dominant because, as Hartley states, many statisticians have first placed their trust in mathematicism: reality is reduced to quantitative functioning. The subjectivist approach fits into the personality ideal and indirect frequentism fits well with this framework. Indirect frequentism absolutises the role of subjective elements, the individual scientist becomes the 'last word concerning the credibility of a hypothesis' (p. 76).

The only paradigm that could provide a Christian basis is then subjectivist Bayesianism. This is then examined, in chapter 7, to see how well it does comport with a Christian worldview. Subjective bayesianism makes no claims that scientific hypotheses 'must follow solely from quantitative data' and it holds to the 'coherence of inter-aspectual meaning' (p 82). Hartley identifies some possible conflicts between the PLI and subjective bayesianism but these are not insurmountable. Though he rejects the other three paradigms as being inconsitent with a Christian perspective, he does note that they could be implemented non-reductively and their results may 'approximate subjective bayesian conclusions' (p106).

There is a useful six-page glossary of key statistical terms and Dooyeweerdian terms and an eight-page bibliography. Unfortunately, there is no index.

This brief book is not an easy read, nevertheless it demands and repays careful attention. It should be required reading for all statisticians, mathematicans and scientists. It provides an excellent role model for the application of Dooyeweerd's philosophy to a subject and has shown how religious belief control statistical inference. Statistics is not religiously neutral. It isn't the last word on Christianity and statistics - as Hartley notes in his conclusion, where he identifies other areas for reflection and investigation (p 111) - but it is an important step towards it. It is a pioneering book and will provide the basis for much needed research and discussion.